Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Simplify.

[tex]\[
\left(\frac{3}{4} \sqrt{15}\right)(16 \sqrt{5})
\][/tex]


Sagot :

Let's break down the expression step by step and simplify it.

Given expression:
[tex]\[ \left(\frac{3}{4} \sqrt{15}\right)\left(16 \sqrt{5}\right) \][/tex]

1. Separate the constants and radicals:
[tex]\[ \left(\frac{3}{4}\right) \cdot 16 \quad \text{and} \quad \sqrt{15} \cdot \sqrt{5} \][/tex]

2. Simplify the constants:
[tex]\[ \left(\frac{3}{4}\right) \cdot 16 = \frac{3 \cdot 16}{4} = \frac{48}{4} = 12 \][/tex]

3. Combine the radicals:
[tex]\[ \sqrt{15} \cdot \sqrt{5} = \sqrt{15 \times 5} = \sqrt{75} \][/tex]

4. Simplify the radical [tex]\(\sqrt{75}\)[/tex]:
[tex]\[ \sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \cdot \sqrt{3} = 5 \sqrt{3} \][/tex]

5. Combine the simplified constants and radicals:
[tex]\[ 12 \cdot 5 \sqrt{3} = 60 \sqrt{3} \][/tex]

Thus, the simplified expression is:
[tex]\[ 60 \sqrt{3} \][/tex]

To summarize:
- Combine and simplify the constants,
- Combine the radicals and simplify,
- Finally, multiply the simplified constants and radicals to get the final result.
Thus, the answer is [tex]\( 60 \sqrt{3} \)[/tex].
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.